The gas mileage for a car is 23 miles per gallon when the car travels at 60 miles per hour. The car begins a trip with 13 gallons in its tank, travels at an average speed of 60 miles per hour for h hours, and ends the trip with 10 gallons in its tank. Which of the following equations best models this situation? Choose 1 answer: 13-(23 h)/(60)=10 13-(60 h)/(23)=10 (13-60 h)/(23)=10 (13-23 h)/(60)=10

Question

The gas mileage for a car is 23 miles per gallon when the car travels at 60 miles per hour. The car begins a trip with 13 gallons in its tank, travels at an average speed of 60 miles per hour for  h hours, and ends the trip with 10 gallons in its tank. Which of the following equations best models this situation? Choose 1 answer:  13-(23 h)/(60)=10  13-(60 h)/(23)=10  (13-60 h)/(23)=10  (13-23 h)/(60)=10

Bytelearn · Accepted Answer

Gas Usage Calculation: We need to determine how much gas the car uses over h hours when traveling at 60 miles per hour. The car's gas mileage is 23 miles per gallon, which means for every hour the car travels at 60 miles per hour, it uses 60/23 gallons of gas. Since the car starts with 13 gallons and ends with 10 gallons, the amount of gas used is 13 - 10 = 3 gallons. We need to find the value of h that corresponds to this usage.Equation Setup: To find the number of hours h that the car traveled, we can set up an equation where the total gallons used (13 - 10) equals the gallons used per hour (60/23) times the number of hours h. This gives us the equation 13 - (60/23)h = 10.Equation Verification: We can check the equation by plugging in the values. If h is the number of hours the car traveled, then (60/23)h should give us the number of gallons used. Since the car used 3 gallons (13 - 10), we can check if (60/23)h equals 3 when h is the correct number of hours. If we solve the equation for h, we should get a reasonable number that, when multiplied by (60/23), gives us 3.

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